带有不同权函数的退化拟线性椭圆方程弱解的Holder正则性

我们研究了一类系数依赖于两不同权函数的退化拟线性椭圆方程．利用加权Sobolev不等式,加权Poincare不等式及Moser迭代技巧,得到了非负弱解的Harnack不等式,证明了弱解的H61der连续性．     

与广义Baouendi-Grushin向量场相联系的Hardy不等式及其应用

本文建立一类与广义Baouendi—Grushin向量场联系的Hardy不等式．采用的技巧是延伸欧氏空间上的散度定理推出的基本积分不等式和选定适当的向量场．Hardy不等式相应的最佳常数也得到证明．本文结果包括了已有广义Baouendi-Grushin向量场的Hardy不等式．作为应用，讨论了由Baouendi-GrusMn向量场构成一退化次椭圆算子的一些性质和刻画了这类向量场构成的非线性算子的一个正解．     

Becker-Stark不等式与Ste(c)kin不等式

若Becker-Stark不等式成立，则Steckin不等式一定成立．使用微分法或幂级数法可证明Steckin不等式．     

弱Orlicz鞅空间的极大不等式

本文研究了弱Orlicz鞅空间的双Φ-不等式．利用鞅的极大算子理论和弱Orlicz范数的特点,得到了弱Orlicz鞅空间极大算子的Doob不等式和强弱(Φ1,Φ2)-型不等式．     

Holder不等式的再推广及应用

文[1]用Jensen不等式得到了推广的Holder不等式（即定理1，字母有变），本文用数学归纳法简证并推广．     

Schur不等式和Hoelder不等式及其应用

Schur不等式和Hoelder不等式是两个重要的不等式，本讲我们介绍Schur不等式和Hoelder不等式及其应用．     

周期型的Bohr不等式

利用献[1]中非对称逼近的方法得到了周期型Bohr不等式．     

对称扩散过程的对数Sobolev不等式、指数可积性和熵的指数衰减性(英)

本文讨论了对称扩散过程的指数可积性，熵的指数衰减性与Sobolev不等式之间的等价关系．并给出了对称扩散过程的对数Sobolev不等式成立的一个充分条件．     

一类离散双险种风险模型

本研究了一类离散双险种风险模型，其中一类险种的索赔到达为泊松随机序列，另一类险种的索赔到达为二项随机序列．得到了最终破产概率的Lundberg不等式以及一般表达式．     

Minc—Sathre不等式的改进

本文利用一个与Gamma函数有关的函数的几何凸性．得到了一个新的不等式．它加强了Minc—Sathre不等式和H。Alzer的推广不等式．     

The Moser-Trudinger-Onofri Inequality

This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or the Onofri inequality for brevity. In dimension two this inequality plays a role similar to that of the Sobolev inequality in higher dimensions. After justifying this statement by recovering the Onofri inequality through various limiting procedures and after reviewing some known results, the authors state several elementary remarks. Various new results are also proved in this paper. A proof of the inequality is given by using mass transportation methods (in the radial case), consistently with similar results for Sobolev inequalities. The authors investigate how duality can be used to improve the Onofri inequality, in connection with the logarithmic Hardy-Littlewood-Sobolev inequality. In the framework of fast diffusion equations, it is established that the inequality is an entropy-entropy production inequality, which provides an integral remainder term. Finally, a proof of the inequality based on rigidity methods is given and a related nonlinear flow is introduced.     

REFINEMENTS OF THE FAN－TODD‘S INEQUALITIES

51. IntroductionIn recent years, refinements or interpolations have played an important role on severaltypes of inequalities with new results deduced as a consequence. Please refer to the papers[2, 8, 9, 12], etc. The aim of this paper is to furnish refinements of the Cauchy's and Bessel'sinequalties as shown in Section 2, and also refinements of the Fan-Todd's inequality and theFan-Todd's determinantal inequality in Sections 3 and 4, with an improved condition forequality derived.First of…     

REFINEMENTS OF THE FAN-TODD'S INEQUALITIES

Refinements to inequalities on inner product spaces are presented. In this respect, inequalities dealt with in this paper are: Cauchy's inequality, Bessel's inequality, Fan-Todd's inequality and Fan-Todd's determinantal inequality. In each case, a strictly increasing function is put forward, which lies between the smaller and the larger quantities of each inequality. As a result, an improved condition for equality of the Fan-Todd's determinantal inequality is deduced.     

Two new forms of half-discrete Hilbert inequality

In this paper, we introduce two new forms of the half-discrete Hilbert inequality. The first form is a sharper form of the half-discrete Hilbert inequality and is related to Hardy inequality. In the second one, we give a differential form of this inequality.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的Holder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式，而在于发现新的不等式．     

On a reverse Heinz–Kato–Furuta inequality

In the set up of Minkowski spaces, the Schwarz inequality holds with the reverse inequality sign. As a consequence, the same occurs with the triangle inequality. In this note, extensions of this indefinite version of the Schwarz inequality are presented. Namely, a reverse Heinz–Kato–Furuta inequality valid for timelike vectors is included and related inequalities that also hold with the reverse sign are investigated.     

Local Poincaré inequalities in non-negative curvature and finite dimension

In this paper, we derive a new set of Poincaré inequalities on the sphere, with respect to some Markov kernels parameterized by a point in the ball. When this point goes to the boundary, those Poincaré inequalities are shown to give the curvature-dimension inequality of the sphere, and when it is at the center they reduce to the usual Poincaré inequality. We then extend them to Riemannian manifolds, giving a sequence of inequalities which are equivalent to the curvature-dimension inequality, and interpolate between this inequality and the Poincaré inequality for the invariant measure. This inequality is optimal in the case of the spheres.     

Szasz不等式在亚正定矩阵和拟广义正定矩阵上的推广

实对称正定矩阵的Szasz不等式是Hadamard不等式的加细;本文将Szasz不等式推广到一类亚正定矩阵和拟广义正定矩阵上去,从而推广了关于实对称正定矩阵的Szasz不等式和Hadamard不等式.     

HARDY-SOBOLEV INEQUALITIES WITH GENERAL WEIGHTS AND REMAINDER TERMS

The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature.     

On the cardinality of Urysohn spaces

Recently, in Cammaroto et al. (2013) [4] we obtained a generalization of the famous inequality established by A.V. Arhangel?ski? in 1969 for Hausdoff spaces. In this paper, following this line of research, we present a common variation of this inequality for Urysohn spaces by developing a Main Theorem for obtaining inequalities. In particular, we extend a 2006 inequality by Hodel for Urysohn spaces. Moreover, this extended inequality is used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality and this new result solves an open problem in Cammaroto et al. (2013) [4] for Urysohn spaces. This general theorem also provides a new cardinal inequality for Hausdorff spaces. The paper is concluded with some open problems.